I want to cast Major Illusion just outside a window to make an illusion of part of the sun.
You can't create sufficient heat or cold to cause damage, a sound loud enough to deal thunder damage or deafen a creature, or a smell that might sicken a creature (like a troglodyte's stench).
The spell description does not specify it can't be as powerful (so bright that it's blinding, or whatever cause the disadvantage) as the sunlight.
Will a creature with Sunlight Sensitivity get disadvantage when fighting under the illusory sunlight?
Similarly, will a vampire takes damage under this illusory sunlight?
There is a precedence in Tomb of Annihilation, pg. 141, that sunlight cast by illusory magic still affects creatures averse to sunlight:
Illusion magic generates the sunlight [...] This light is treated as real sunlight, and creatures averse to sunlight are affected by it.